Question: The sum of two numbers is $45$, and their difference is $5$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 45}$ ${x-y = 5}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 50 $ $ x = \dfrac{50}{2} $ ${x = 25}$ Now that you know ${x = 25}$ , plug it back into $ {x+y = 45}$ to find $y$ ${(25)}{ + y = 45}$ ${y = 20}$ You can also plug ${x = 25}$ into $ {x-y = 5}$ and get the same answer for $y$ ${(25)}{ - y = 5}$ ${y = 20}$ Therefore, the larger number is $25$, and the smaller number is $20$.